Rotor unmanned aerial vehicle cluster hanging system acceleration feasible space calculation method

Abstract

This invention discloses a method for calculating the feasible space of acceleration in a rotorcraft UAV swarm sling system. It establishes a dynamic model of the load based on the system's spatial configuration and determines the range of tension based on the aircraft's load capacity and cable pretension. It establishes the incremental form of the tension on the load and then, given a traversal matrix, traverses the vertices of the acceleration convex hull space to characterize the feasible space. Considering external disturbances with bounded norms and unknown directions, the disturbances are mapped to a sphere G in the nominal space, and the robust feasible space of load acceleration is calculated by incorporating the sphere G. This invention fully considers factors such as system configuration, aircraft load capacity, cable pretension, and external environmental disturbances, proposing a set of algorithms for solving the load acceleration of a UAV swarm sling system. When the acceleration is within the feasible space, the acceleration within the space can ensure that the cable is under rigid conditions, and this algorithm is applicable to UAV swarm systems of any sortie rate, exhibiting stronger applicability.

Description

Technical Field

[0001] This invention relates to automatic control technology, and in particular to a method for calculating the feasible space of acceleration in a rotary-wing unmanned aerial vehicle (UAV) swarm sling system. Background Technology

[0002] Rotary-wing drones are a widely used type of unmanned aerial vehicle, extensively applied in aerial photography, transportation, and exploration. Among these applications, sling transport is a significant research area. This method involves connecting a single drone to the transported item via a rope, allowing for rapid transport through aerial flight. It eliminates the need to consider the complexities of terrain such as mountains and forests, demonstrating immense potential and advantages in transportation. However, as the types of transported goods become increasingly complex, traditional single drones are no longer sufficient. The rise of swarm drone technology has led to the concept of cluster sling transport. Compared to single drones, sling transport offers a significant leap in load capacity, capable of lifting weights several times, even hundreds of times, that of a single drone. However, sling transport systems have a higher degree of coupling than single-drone systems, posing considerable challenges to control.

[0003] Current research on control of multi-drone sling loads primarily relies on modeling and controlling the cables as rigid bodies or treating load motion as a disturbance. This approach suffers from several drawbacks: the former fails to account for actual cable flexibility, resulting in ineffective control and potentially exacerbating load sway; the latter neglects to analyze a reasonable flight space, merely treating load motion as interference with the drones. When the system experiences external disturbances or performs maneuvers exceeding this reasonable flight space, cable deformation and excessive swaying inevitably lead to system instability. Therefore, a method for calculating load acceleration in multi-drone sling load systems is urgently needed to ensure system stability. Furthermore, the feasible space for load acceleration is highly dependent on the number of drone sling operations; as the number of operations increases, the complexity of conventional optimization methods becomes unsolvable. Summary of the Invention

[0004] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a feasible acceleration space calculation method for a rotary-wing UAV swarm sling system. This method calculates the acceleration space where the ropes do not undergo flexible deformation, thus ensuring the ropes remain taut and the system remains stable, especially when multiple UAVs are slinged together and the resulting ropes are flexible.

[0005] Technical solution: The present invention provides a method for calculating the feasible space of acceleration for a rotary-wing unmanned aerial vehicle (UAV) swarm suspension system, comprising the following steps:

[0006] S10: Establish a dynamic model of the load based on the spatial configuration of the UAV cluster and the load, determine the range of tension based on the aircraft's load capacity and cable preload, and give the incremental form of the total tension.

[0007] S20, the nominal feasible space of load acceleration is calculated based on the incremental form of the total tensile force design algorithm, and is denoted as the nominal feasible space of load acceleration;

[0008] S30. Introduce an interference force into the suspension system and map the interference to a sphere G in the nominal feasible space. Make the sphere G move inward in the nominal feasible space. Design an algorithm to calculate the reachable space of the sphere's center, which is denoted as the robust feasible space of the load acceleration under the action of the interference force.

[0009] Furthermore, the dynamic model expression for the load is:

[0010]

[0011] In the formula, i = 1, 2, ..., N represents the i-th rope, N represents the total number of ropes, and F i θ represents the tension in the i-th rope. i The longitudinal angle represents the rotation angle of rope i in the vertical plane, m represents the mass of the load, g represents the acceleration due to gravity, and a x a y and γ represents the acceleration of the load along the X, Y, and Z axes of the inertial frame, respectively. i The horizontal angle represents the angle between the projection of rope i onto the horizontal plane and the X-axis;

[0012] The total tensile force F exerted on the load by all UAVs within the suspension system, calculated based on the load's dynamic model, is expressed as:

[0013]

[0014] In the formula, vector Characterizes the direction of tension in rope i; Represents a three-dimensional column vector;

[0015] At the same time, the tension F on rope i i The following inequality relationships should be satisfied:

[0016] F i-min ≤F i ≤F i-max

[0017] In the formula, F i-min F represents the minimum preload required to stiffen the i-th rope. i-max This represents the maximum tension provided by the i-th drone to the i-th rope;

[0018] The tension F in each rope i Rewritten in incremental form, the expression is:

[0019] F i =F i-min +λ i ΔF i

[0020] In the formula, ΔF i The tensile force is expressed as ΔF. i =F i-max -F i-min ;λ i λ is the normalization factor. i ∈[0,1];

[0021] The total tensile force F can be rewritten in incremental form as follows:

[0022]

[0023] The spatial form of the total tensile force F is expressed as F s The expression is:

[0024]

[0025] In the formula, F min This represents the minimum tension vector. w represents the spatial configuration matrix. ΔF represents the tensile force vector. Λ represents the traversal of the matrix, expressed as:

[0026] Λ = [Binary] N (0)Binary N (1)…Binary N (2 N -1)]

[0027] Among them, Binary N (·) represents a function that converts a decimal number into an N-bit binary column vector and expands it column by column;

[0028] Let the feasible space for load acceleration be denoted as Then we have:

[0029]

[0030] Substituting the incremental total tension F into the above equation, we obtain the feasible space expression for the load acceleration as follows:

[0031]

[0032] In the formula, a j for The column vectors represent the vertices of the feasible space for load acceleration, j = 1, 2, ..., 2. N g is the acceleration due to gravity.

[0033] Furthermore, the feasible space for load acceleration under disturbing forces is denoted as the robust space. Considering the boundedness of the disturbance force d, the range of values ​​for the disturbance force can be expressed as: ‖d‖≤d max , where d max Let represent the maximum disturbance force. Then, the effect of the disturbance force on the load acceleration is expressed as: ‖d / m‖;

[0034] Based on the incremental form of the total tensile force, the nominal space vertices point towards the center of the space. vector matrix Each column of matrix E represents the direction vector from the corresponding vertex to the spatial center O, and the calculation formula is as follows:

[0035]

[0036] With the center of space O as the center of the sphere, the nominal space is... The radius of the largest inscribed sphere is R, and the radius of the smaller inscribed sphere is r = d. max / m, then robust space The calculation formula is:

[0037]

[0038] Furthermore, the nominal space is solved using the bisection method. The maximum inscribed sphere radius is an approximation of R', which includes:

[0039] Initialization: Define initial value R min and R max R min =0, R max Let R be the distance from the center O of space to any vertex. max If the radius of the maximum inscribed sphere is greater than the true value R, set the loop termination condition to R. max -R min <γ;

[0040] Enter the loop: Check if the radius is (R) max +R min Is the sphere of θ2 in nominal space? Inside, if in the nominal space Then update R min =(R max +R min )θ2; otherwise, update R. max =(R max +R min)θ2;

[0041] End: After the loop terminates, let R′ = R min Replacing R with R′ yields the actual robust space obtained. The expression is:

[0042]

[0043] Beneficial Effects: Compared with the prior art, the significant advantages of this invention are as follows: Based on the feasible space analysis of acceleration for a rotorcraft UAV swarm slinging system, this invention fully considers factors such as system configuration, aircraft load capacity, rope pretension, and external environmental interference, and proposes a solution for calculating acceleration. When the acceleration is within the feasible space, the rope can be kept under rigid conditions, which can be used as the maneuvering requirement during slinging flight. By limiting the rope tension to a specific range, the maximum value of which is the maximum tension that the UAV can provide to the rope or the maximum tension that the rope can withstand, and the minimum value is the minimum pretension that ensures the rope is in a taut state, the rope is kept taut throughout the movement. This method is also applicable to sling transport scenarios with a large number of UAVs and can greatly ensure the stability of the slinging system. Attached Figure Description

[0044] Figure 1 This is a diagram of a multi-machine suspension structure;

[0045] Figure 2 This is a schematic diagram of the nominal space and the robust space;

[0046] Figure 3 This is a flowchart of robust space computation. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0048] The acceleration feasible space calculation method for a rotary-wing UAV swarm sling system described in this embodiment includes the following steps:

[0049] S10: Establish a dynamic model of the load based on the spatial configuration of the UAV cluster and the load, determine the range of tension based on the aircraft's load capacity and cable preload, and give the incremental form of the total tension.

[0050] The dynamic model expression for the load is:

[0051]

[0052] In the formula, i = 1, 2, ..., N represents the i-th rope, N represents the total number of ropes, and Fi θ represents the tension in the i-th rope. i The longitudinal angle represents the rotation angle of rope i in the vertical plane, such as... Figure 1 As shown in the multi-machine hoisting structure diagram, among which Figure 1 Taking the example of three drones suspending a load, m represents the acceleration of the load, g represents the acceleration due to gravity, and a x a y and Representing the projections of the load acceleration onto the X, Y, and Z axes of the inertial frame, respectively, γ i The horizontal angle represents the angle between the projection of rope i onto the horizontal plane and the X-axis.

[0053] The total tensile force F exerted on the load by all UAVs within the suspension system, calculated based on the load's dynamic model, is expressed as:

[0054]

[0055] In the formula, vector Characterizes the direction of tension in rope i; Represents a three-dimensional column vector;

[0056] At the same time, the tension F on rope i i The following inequality relationships should be satisfied:

[0057] F i-min ≤F i ≤F i-max

[0058] In the formula, F i-min F represents the minimum preload required to stiffen the i-th rope. i-max F represents the maximum tension provided by the i-th drone to the i-th rope. i-min and F i-max All are known quantities, and F i-min >0, F i-max >0.

[0059] The tension F in each rope i Rewritten in incremental form, the expression is:

[0060] F i =F i-min +λ i ΔF i

[0061] In the formula, ΔF i The tensile force is expressed as ΔF. i =F i-max -F i-min ;λ i λ represents the normalization factor. i ∈[0,1].

[0062] The total tension F can be rewritten in incremental form by expressing the increment of tension in each rope as follows:

[0063]

[0064] Since the total tension F is composed of multiple vectors, it can be analyzed that the vertices of the tension space of F must be composed of multiple vectors arranged and combined, and must be the convex hull formed by the vertices we are looking for. Therefore, the tension space problem is transformed into solving a multi-vertex problem.

[0065] Since the spatial configuration of the entire suspension system has been specified in advance by the user, i.e., q i If all are known constant vectors, then It can be composed of 2 N The convex hull space is formed by 8 vertices. In one embodiment, when the number of drones is 3, i.e., N=3, a convex hull space can be formed by 8 vertices, such as... Figure 2 The cube formed by the midpoints A1 to A8 is the feasible space for load acceleration.

[0066] S20, the nominal feasible space of load acceleration is calculated based on the incremental form of the total tension using an algorithm, and is denoted as the nominal feasible space of load acceleration.

[0067] Specifically, the spatial form of the total tensile force F is expressed as F s The expression is:

[0068]

[0069] The total tensile force F exerted by the drone on the load is variable. This variable can be expressed as F... s To represent, F min This represents the minimum tension vector. w represents the spatial configuration matrix. ΔF represents the tensile force vector. Λ represents the traversal of the matrix, expressed as:

[0070] Λ = [Binary] N (0)Binary N (1)…Binary N (2 N -1)]

[0071] Among them, Binary NThis represents a function that converts a decimal number to an N-bit binary number, expanded column-wise, where each element is still a decimal number, consisting of 0 and 1 in decimal, where 0 indicates the vector is not selected and 1 indicates it is selected. In this embodiment, taking three drones as an example, the λ of each vertex in the convex hull space... i The values ​​are shown in Table 1. Then, the matrix is ​​iterated through...

[0072] The operation of row vector · matrix has the highest priority, and the operation rules are as follows:

[0073]

[0074] Table 1. λ of each vertex in the convex hull space i value

[0075] <![CDATA[λ1]]> 0 0 0 0 1 1 1 1 <![CDATA[λ2]]> 0 0 1 1 0 0 1 1 <![CDATA[λ3]]> 0 1 0 1 0 1 0 1

[0076] Let the feasible space for load acceleration be denoted as Then we have:

[0077]

[0078] Substituting the incremental total tension F into the above equation, we obtain the feasible space expression for the load acceleration as follows:

[0079]

[0080] In the formula, a j for The column vectors simultaneously represent the vertices of the feasible space for load acceleration, and... Figure 2 The numbers A1 to A8 correspond to each other, j = 1, 2, ..., 2 N g is the acceleration due to gravity.

[0081] For A8, j = 1, 2, ..., 2 N ; g is the acceleration due to gravity; S30, introduce an interference force into the suspension system, map the interference to a sphere G in the nominal space, and make the sphere G make an internal tangent motion in the nominal space. Design an algorithm to calculate the reachable space of the sphere's center, which is denoted as the robust feasible space of the load acceleration under the action of the interference force.

[0082] Due to the uncertainty of the direction of interference, the interference force is analogous to a sphere G in three-dimensional space to ensure coverage of every direction in the space. The radius of the sphere G is the effect of the maximum interference force on the acceleration, i.e., radius r = d. max / m. The robust space is the space within which the center of the sphere G can be tangent to the nominal space. For example... Figure 2 The internal cube represents the feasible space for load acceleration when considering the disturbance force, and the inscribed sphere is the sphere G.

[0083] Denote the feasible space of the load acceleration with interference force as the robust space Considering the boundedness of the interference force d, represent the value range of the interference force as: ‖d‖ ≤ d max , where d max represents the maximum interference force, and the influence of the interference force on the load acceleration is expressed as: ‖d / m‖.

[0084] It can be proved that there exists a centrosymmetric point for the vertices of the convex hull space obtained in step S20. The proof is as follows:

[0085] Assume the starting point is P. For any vertex P1 = P+(ΔF1q1+…), there always exists a corresponding vertex So the midpoint is always And for any vertex P1, the vector pointing to the midpoint O is And

[0086] According to this, based on the traversal matrix Λ in step S20, translate the traversal matrix Λ 0.5 units in the negative direction to become a new change matrix Γ. The expression is:

[0087]

[0088] Then the vector from the corresponding vertex to the center O is E = -ΔF·wΓ. The j-th column of the matrix E represents the vector from the j-th vertex to the center. <00,00381>[[ID=3,4]]Now, with the center O as the center of the sphere, find the maximum radius R such that the sphere is inside the nominal space There are the following situations:

[0090] When a small sphere with a radius of r (r < R) is placed inside the nominal space Assume the center of the small sphere is O'. When is satisfied (P1 is any vertex), then this small sphere must be inside the nominal space Then the coordinates of the corresponding vertex scaled inward can be obtained through this algorithm and used as the vertices of the robust space. Using the binary approximation method, after a given determination accuracy value γ > 0, the approximate value R' of the maximum radius R can be quickly obtained, and then the robust space can be obtained according to the ratio.

[0091] Calculate the vector matrix from each vertex of the nominal space to the center of the space according to the total tension in incremental form Each column of the E matrix represents the direction vector from the corresponding vertex to the center of the space O. The calculation formula is as follows:

[0092] ​

[0093] With the center of space O as the center of the sphere, the nominal space is... The radius of the largest inscribed sphere is R, and the radius of the smaller inscribed sphere is r = d. max / m, then robust space The calculation formula is:

[0094]

[0095] Specifically, the nominal space is solved using the bisection method. The maximum inscribed sphere radius is an approximation of R', as shown in the flowchart. Figure 3 As shown, specifically:

[0096] - Initialization: Define the initial value R min and R max R min =0, R max Let R be the distance from the center O of space to any vertex. max If the radius of the maximum inscribed sphere is greater than the true value R, set the loop termination condition to R. max -R min <γ;

[0097] - Enter the loop: Check if the radius is (R) max +R min Is the ball of 1 / 2 in nominal space? Inside, if in the nominal space Then update R min =(R max +R min ) / 2; otherwise, update R. max =(R max +R min ) / 2;

[0098] -End: After the loop terminates, let R′ = R min Replacing R with R′ yields the actual robust space obtained. The expression is:

[0099]

[0100] Current research on drone swarm slinging systems almost entirely relies on rope rigidity analysis. Failure to meet this rigidity requirement can lead to system instability and severe consequences. This invention addresses this by analyzing the acceleration feasibility space of a rotorcraft drone swarm slinging system. It fully considers factors such as system configuration, aircraft load capacity, rope preload, and external environmental interference, providing a solution for calculating acceleration. When the acceleration is within the feasible space, the rope remains rigid, thus fulfilling the maneuverability requirements for swarm slinging flight.

Claims

1. A method for calculating the feasible space of acceleration for a rotary-wing UAV swarm sling system, characterized in that, Includes the following steps: S10: Establish a dynamic model of the load based on the spatial configuration of the UAV cluster and the load, determine the range of tension based on the aircraft's load capacity and cable preload, and give the incremental form of the total tension. S20, calculate the nominal feasible space of load acceleration based on the incremental form of total tension design algorithm; S30, introduce an interference force into the suspension system, map the interference to a sphere G in the nominal feasible space, and make the sphere G make an internal tangential motion in the nominal feasible space. Design an algorithm to calculate the reachable space of the sphere center, which is denoted as the robust feasible space of the load acceleration under the action of the interference force. The spatial form of the total tensile force F is expressed as: The expression is: ； In the formula, This represents the minimum tension vector. ; Represents the spatial configuration matrix. Indicates the total number of ropes. , Characterizes the direction of tension in rope i; Represents the tensile force vector. ; Indicates the tensile force; To traverse a matrix, the expression is: ； in, This function converts a decimal number into an N-bit binary column vector and expands it column by column. Let the feasible space for load acceleration be denoted as Then we have: ； in, Indicates the quality of the load. Represents gravitational acceleration; The total tension of spatial form Substituting into the above equation, we obtain the feasible space expression for load acceleration as follows: ； In the formula, for The column vectors simultaneously represent the vertices of the feasible space for load acceleration. ; It is gravitational acceleration.

2. The acceleration feasible space calculation method according to claim 1, characterized in that, The dynamic model expression of the load in step S10 is: ； In the formula, This represents the i-th rope. Indicates the total number of ropes. This represents the tension in the i-th rope. The vertical angle represents the rope. Rotation angle in the vertical plane Indicates the quality of the load. Represents gravitational acceleration. These represent the load in the inertial frame. , , Acceleration on the axis, The horizontal angle represents the rope. Projection on the horizontal plane and The included angle of the axis; The total tensile force F exerted on the load by all UAVs within the suspension system, calculated based on the load's dynamic model, is expressed as: ； In the formula, vector Characterizes the direction of tension in rope i; Represents a three-dimensional column vector; Meanwhile, rope The tension on The following inequality relationships should be satisfied: ； In the formula, Indicates the first The minimum preload for the rigidity of a rope. Indicates the first The drone was provided to the first The maximum tension of the rope; The tension of each rope Rewritten in incremental form, the expression is: ； In the formula, Indicates the tensile force. ; As the normalization factor, ; The total tensile force F can be rewritten in incremental form as follows:

3. The acceleration feasible space calculation method according to claim 2, characterized in that, The feasible space for load acceleration under disturbing forces is denoted as the robust space. Considering interference The boundedness of the disturbance force allows us to express its range as follows: ,in Let represent the maximum disturbance force. Then, the effect of the disturbance force on the load acceleration is expressed as: ; Based on the incremental form of the total tensile force, the nominal space vertices point towards the center of the space. vector matrix ,in Each column of the matrix represents the direction from the corresponding vertex to the center of space. The direction vector is calculated using the following formula: ； With space center Center of the sphere, nominal space The maximum radius of the inscribed sphere is The radius of the inscribed sphere is Then robust space The calculation formula is:

4. The acceleration feasible space calculation method according to claim 3, characterized in that, Solving the nominal space using the bisection method The maximum radius of the inscribed sphere is approximation ,include: Initialization: Define initial values and , , As the center of space The distance to any vertex, at this time Greater than the true value of the maximum inscribed sphere radius Set the loop termination condition as ; Enter the loop: Check if the radius is Is the ball in nominal space? Inside, if in the nominal space Then update Conversely, update. ; End: After the loop terminates, set ,use replace Obtain the actual robust space The expression is:

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